178
12 High-Precision Differential Photometry
the data, that is an indication of a problem with one or more of the check stars. Even
if there is no indication of a problem, it is good practice to plot each of the check
stars along with the mean. If they are significantly different from the mean, they
should be removed from the sample and the mean recalculated. Likewise, if there is
a change in brightness in one target star that is not reflected in the others (although
it will be reflected in the mean), that should also be removed. What will remain after
several iterations of this process is a set of check stars that are representative of the
conditions being observed.
The photometric uncertainty is then
m =
σ
2
ref +
N
√
N
2
,
(12.5)
where σ ref is the standard deviation between the count in the check stars and the mean
count of the check stars, and N is the count of the target.
12.8 Postmeasurement Uncertainty Reduction and Light
Curve Folding
As we have seen in this chapter, there are many sources of noise in photometric
systems, and by careful calibration and planning, you should have managed to reduce
the uncertainties to the point that the signal-to-noise ratio is great enough for an
observation to be successful. If that is not the case, there is a single course open
to you: to sacrifice cadence in order to improve photometric accuracy. However, be
aware that by doing so, you will increase the time-series uncertainties, which are
the times between the start of one frame and the start of another (not the exposure
time), which might result in some important features in the light curve being lost.
By binning adjacent data points, taking the mean of the two points, the uncertainty
is reduced by 70%.
If you are observing a regularly occurring feature such as an eclipsing variable
or an exoplanet transit, an alternative method to improve photometric accuracy is
light curve folding. Light curve folding works by overlaying repeated observations
on a single curve. For this to happen, you need to identify a feature that occurs in
all the light curves, which typically will be a contact shoulder but not always. Note
the chronological position of this feature in each of the light curves; the FITS header
should have this as a Julian date. If you know the period between events, you can fold
the light curve into phase space. This can be done in a programming language like
Python or simply in a spreadsheet. The data point with the lowest Julian date (i.e.,
the first one taken) is used as the anchor point in this illustration. It can be changed if
you wish. We shall call the Julian date of this observation t 0 . We can now determine
the phase space of all other data points using
12 High-Precision Differential Photometry
the data, that is an indication of a problem with one or more of the check stars. Even
if there is no indication of a problem, it is good practice to plot each of the check
stars along with the mean. If they are significantly different from the mean, they
should be removed from the sample and the mean recalculated. Likewise, if there is
a change in brightness in one target star that is not reflected in the others (although
it will be reflected in the mean), that should also be removed. What will remain after
several iterations of this process is a set of check stars that are representative of the
conditions being observed.
The photometric uncertainty is then
m =
σ
2
ref +
N
√
N
2
,
(12.5)
where σ ref is the standard deviation between the count in the check stars and the mean
count of the check stars, and N is the count of the target.
12.8 Postmeasurement Uncertainty Reduction and Light
Curve Folding
As we have seen in this chapter, there are many sources of noise in photometric
systems, and by careful calibration and planning, you should have managed to reduce
the uncertainties to the point that the signal-to-noise ratio is great enough for an
observation to be successful. If that is not the case, there is a single course open
to you: to sacrifice cadence in order to improve photometric accuracy. However, be
aware that by doing so, you will increase the time-series uncertainties, which are
the times between the start of one frame and the start of another (not the exposure
time), which might result in some important features in the light curve being lost.
By binning adjacent data points, taking the mean of the two points, the uncertainty
is reduced by 70%.
If you are observing a regularly occurring feature such as an eclipsing variable
or an exoplanet transit, an alternative method to improve photometric accuracy is
light curve folding. Light curve folding works by overlaying repeated observations
on a single curve. For this to happen, you need to identify a feature that occurs in
all the light curves, which typically will be a contact shoulder but not always. Note
the chronological position of this feature in each of the light curves; the FITS header
should have this as a Julian date. If you know the period between events, you can fold
the light curve into phase space. This can be done in a programming language like
Python or simply in a spreadsheet. The data point with the lowest Julian date (i.e.,
the first one taken) is used as the anchor point in this illustration. It can be changed if
you wish. We shall call the Julian date of this observation t 0 . We can now determine
the phase space of all other data points using